Question 15 Find the domain of \( f(x)=\sqrt{x-2} \) Use two lower case o's for infinity. "oo" is how you type in infinity. Question Help: Video \( \square \) Message instructor Submit Question Question 16

To find the domain of the function \( f(x) = \sqrt{x - 2} \), we need to determine the values of \( x \) for which the expression under the square root is non-negative, since the square root of a negative number is not defined in the set of real numbers. ### Step 1: Set the expression under the square root greater than or equal to zero. \[ x - 2 \geq 0 \] ### Step 2: Solve the inequality. To solve for \( x \), we can add 2 to both sides: \[ x \geq 2 \] ### Step 3: Write the domain in interval notation. The solution indicates that \( x \) can take any value greater than or equal to 2. In interval notation, this is expressed as: \[ [2, oo) \] ### Conclusion The domain of the function \( f(x) = \sqrt{x - 2} \) is \( [2, oo) \).